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Complex Numbers

by Robert Waltz

Rated: 18+ · Book · Personal · #1196512

Not for the faint of art.

Complex Numbers

A complex number is expressed in the standard form a + bi, where a and b are real numbers and i is defined by i^2 = -1 (that is, i is the square root of -1). For example, 3 + 2i is a complex number.

The bi term is often referred to as an imaginary number (though this may be misleading, as it is no more "imaginary" than the symbolic abstractions we know as the "real" numbers). Thus, every complex number has a real part, a, and an imaginary part, bi.

Complex numbers are often represented on a graph known as the "complex plane," where the horizontal axis represents the infinity of real numbers, and the vertical axis represents the infinity of imaginary numbers. Thus, each complex number has a unique representation on the complex plane: some closer to real; others, more imaginary. If a = b, the number is equal parts real and imaginary.

Very simple transformations applied to numbers in the complex plane can lead to fractal structures of enormous intricacy and astonishing beauty.

http://www.ddewey.net/mandelbrot/

Signature for Honorable Mentions in 2018 Quill Awards

A signature for exclusive use of winners at the 2019 Quill Awards

Signature for those who have won a Quill Award at the 2020 Quill Awards

Show Recent Comments

10 Most Recent Blog Comments:

Lazy Writer est 4/24/2008

about 22 hours ago
In response to "Revisited: "Exercise""

I will be 75 in July. My stepdaughter gave me a bike because I wanted to ride it again. Well, I started off shaky and stayed shaky...then I fell off it...A passing motorist stopped to help me get up...I have NOT been back on that bike and will not ever again.

🌕 HuntersMoon

a day ago
In response to "Revisited: "Exercise""

So, you're saying that now you pedal your ass differently?

Elisa the Bunny Stik

Apr 27, 2024 at 10:33am
In response to "Pleasure and Pain"

it illustrates why it's important to have people from different backgrounds, with different worldviews, working on scientific research.

This right here is why I get rather irritated by people poo-pooing college these days. I feel like that attitude effectively shits on minority populations that may not have strong finances but do possess persistent curiosity and want to learn about various subjects in-depth. In the 90s, these groups were exclusively told to go to trade schools even if they had the aptitude for college education. Nowadays the blanket "Everyone should consider a trade" mantra employs a more subtle (but still abundant) form of discrimination. I'm so over it.

1 Like

Kåre Enga in Udon Thani

Apr 25, 2024 at 3:16am
In response to "Going to the Dogs"

I have ants in Thailand. Will I miss them in Montana? No.

Would it be nice to have a cat and a dog, here or there? Yes, but I have struggles keeping my neglected plants alive.

Not every situation is suitable for everything or everybody.

Kåre Enga in Udon Thani

Apr 25, 2024 at 3:09am
In response to "Tipped Out"

I don't tip. In my travels I rarely find tipping the norm.

I also don't haggle.

When you add the tip... the true cost of America becomes evident. But what would I know? I travel while others who have double my income can't pay rent.

Kåre Enga in Udon Thani

Apr 25, 2024 at 2:58am
In response to "Reality Cubed"

My dreams may be different from your dreams but if we share them with others then some form of the dream may live on. Regardless, if we don't eat we die. "Joy gives us wings." "Reality bites."

Aiva Raine

Apr 24, 2024 at 4:26pm
In response to "Tipped Out"

Agreed. I'll tip and well, for actual waitstaff at restaurants. I'll tip appropriately for bell-staff who assists with luggage at hotels, the more luggage, the bigger the tip. I'll give a tip to the valet as well. Beyond that- I don't tip. Certainly no tip for the fast food workers, coffee baristas, grocery store clerks, etc.

It annoys me to no end that we're being asked to tip for all kinds of jobs where they are being paid an hourly wage. I've worked as a waitress when I was young and my daughter currently does. In those jobs- she absolutely depends upon proper tipping to make a decent wage. And I hate the fact that she is dependent upon tips to do so.

It leaves women especially at the mercy of arsh**() on whether she wants to accept hostile, negative, sexist, harassing, demeaning, and negative behavior from her customers in order to make a living. It condones people treating their waitstaff like shite in order to get paid. While there is much improvement from the 30 years ago when I was working as a waitress in the skimpy outfits we were forced to wear- it's still an issue at non-chain, independent owned restaurants and diners.

Women are left to the mercies of jerk customers and their only recourse is the manager who they have to hope supports their waitstaff rather than the jerk customer. Tipping should be eliminated. All employees should be paid a livable wage and waitstaff especially should not be dependent upon tolerating crappy to obscene behavior from customers in order to make a living.

But, until that happens- I always tip at least 20% and often times more. Very rarely have I tipped lower and the service in those situations was abysmal and they still got 10%.

1 Like

GeminiGem of House Lannister

Apr 23, 2024 at 6:51pm
In response to "Going to the Dogs"

I don't understand the intersection, either. I lived in a much smaller city and found that having dogs was a hassle (although it didn't stop me), what with the complainey neighbors, the extra licensing, etc. I live in a rural location now and it works great. I can't wrap my head around living in NYC with or without a dog, although I like the idea of a place that issues a canine and supplies upon moving there. Can that please be a thing?

1 Like

Lazy Writer est 4/24/2008

Apr 23, 2024 at 3:31pm
In response to "Going to the Dogs"

I love my little dog...but I live in a biggish house with a fenced backyard.

1 Like

Aennaytte: Free & Wild in GoT

Apr 23, 2024 at 3:14pm
In response to "That's Cole"

I knew and ate Kohlrabi before I ever heard of kale. Kohlrabi is so much better in every way.

That last quoted sentence is hilarious. I am glad that I wasn't bred to be a Brussels Sprout.

1 Like

August 5, 2019 at 12:02am

#963736

Kelpless

https://www.atlasobscura.com/articles/what-is-nori

Whether you like sushi or not (I do), this is a fascinating read.

Though she lived halfway across the world, Kathleen Drew-Baker played a monumental role in saving Japan’s multi-billion dollar nori industry.

The article goes on to describe nori and its history in Japan, which is pretty cool by itself.

But the main part of the story is what caught my attention.

In 1948, shortly after the end of World War II, the nori disappeared. A series of fierce typhoons—coupled with the effects of pollution and industrialization—had ravaged the coast. Unlike past, unlucky years, this time the nori didn’t bounce back the next year.

So first they lose a war, then famine strikes. Any other horsemen want to weigh in?

But then it gets interesting.

But the research needed to revive Japan’s nori had begun 20 years earlier, across the globe in Manchester, England, when Kathleen Drew-Baker was fired. She had been a lecturer in cryptogamic botany at the University of Manchester, but the college did not employ married women.

So, enter our protagonist, a victim of institutionalized sexism... and a subject of the Crown with which Japan had been enemies up until a short time before.

At the time, botany was one of the only sciences considered appropriate for women to enter. “Botany was a safe science for women,” Kassinger says. “It was the one that didn’t involve mathematics or cutting things up.” As a cryptogamic botanist, Drew-Baker studied plants that reproduced by spores, such as ferns. “Ferns were a good idea for women to study because they didn’t have flowers and therefore they didn’t seem to involve sex,” Kassinger says.

What the eukaryotic fuck, sexism?

She goes on to make an important discovery about the life cycle of algae. This discovery turns out to be crucial to Japan re-establishing its seaweed trade.

Despite the financial setback she faced as a married female scientist, she managed to raise two children while conducting her own research and training younger botanists. In 1952, she was elected the first president of the British Phycological Society.

In short, this chick was a badass.

So if you’re in Wales, try some laverbread, the pulpy seaweed paste kneaded from wild laver. And if you’re ever in Uto, stop by Drew-Baker’s memorial, smell the salty, weedy scent of the Ariake, and pay your respects to Japan’s Mother of the Sea.

So the Japanese kelp farmers put up a statue of this badass scientist from a formerly enemy country, and they pay their respects to her every year.

There's still institutional sexism out there, in the US as well as in the UK... and in Japan. It's not as bad as it used to be, though there's a ways to go still. But science doesn't care about your plumbing or where you stick it; nor does it matter to the people whose lives and livelihood you save.

And it's not just all about research. Science is still the best means we have of figuring out how the universe operates, and as Randall Munroe, the artist behind the webcomic xkcd, said, "it works, bitches."

1 Like • Comment

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